If the gravel is smaller than his head I would remove it immediately. It can cause serious health problems if he eats it, and he will try if it's smaller than his head.
Sounds like you are off to a good start but try to upgrade his home as soon as possible. Think 10 gallons of tank per inch of turtle as a guide to his habitat. And go as large as you can now, to avoid needless upgrades later. Koopa only remained in his 10 gallon almost 4 months and even then that was probably too long. He's now in a thirty gallon that more than likely will need to be upgraded within the next few months, so I am already checking classifieds, etc for a good priced larger tank that he'll need. And take time to research online for your purchases prior to heading to the "pet store", you can usually find much better deals online.
The water temp at 78 is perfect for a hatchling like you have, but after a year old or so 72-75 is recommended for older turtles with the basking temp around 90.
Shrimp treats are okay occasionally (about once a month) and the pellets sound good. How many veggies do you give? It's important to start them on veggies even when they are young and may not take to it immediatly. Veggies will provide a good source of vitamins and help give him a healthy balanced diet that he needs. There's a list under the feeding section of what to feed and not to feed. Also, providing cuttlebone is good for their calcium intake and will help keep their shells healthy when they bask under their UVB light.
